For points of intersection
Area between the curves
(1 point) Book Problem 10 Consider the region between the graphs x = y2 – 7...
Consider the following equations y y2 Sketch the region bounded by the graphs of the equations Find the area of the region Submit Antwer
(1 point) Consider the function defined by F(x, y) = x2 + y2 except at (r, y) - (0, 0) where F(0,0)0 Then we have (0,0) = (0,0) = ax dy Note that the answers are different. The existence and continuity of all second partials in a region around a point guarantees the equality of the two mixed second derivatives at the point. In the above case, continuity fails at (0,0) Note: You can earn partial credit on this problem...
(1 point) Book Problem 3 Find the volume V of the solid obtained by rotating the region bounded by the curves x = 5/, x = 0, y = 8; about the y-axis. V= S hly)dy where a = b = , h(y) = V=
(1 point) Consider the area shown below. The curve drawn is x2 + y2 = 2, and we have used the notation Dy for Ay. (Click on the figure for a larger version.) Write a Riemann sum for the area, using the strip shown: Riemann sum= E Now write an integral that gives this area so where a = and b = Finally, calculate the exact area of the region, using your integral area =
Hi, I need help solving number 13. Please show all the steps,
thank you. :)
Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
Problem 8. Evaluate Jo y' dz + 3zy dy, where C is the boundary of the semianmulan region D in the upper half-plane between the circles x2 + y2 = 1 and x2 + y-4. ANSWERS.
Problem 8. Evaluate Jo y' dz + 3zy dy, where C is the boundary of the semianmulan region D in the upper half-plane between the circles x2 + y2 = 1 and x2 + y-4. ANSWERS.
5 pts) Consider the region bounded by the curves y 9, y and r 1 r-+64 If this region is revolved around the x - axis, the volume of the resulting solid can be computed in (at least) two different ways using integrals. (Sketching the graph of the situation m (a) First of all it can be computed as a single integral h(r)dr where o and This method is commonly called the method of Enter 'DW' for Disks/Washers or 'CS...
1 point) Book Problem 1 (x) x5 x-5 g(x> 0.8a2 8 Set up an integral to find the area A of the region enclosed between f(x) and g(x) -5 to x = 5, and then evaluate it. = x from T= da A - (1 point) Book Problem 39 The base of a certain solid is an elliptical region with boundary curve 4x2 25y2 100. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. A(x)...
(1 point) The volume of the solid obtained by rotating the region bounded by y = x, y = 10x, about the line x = 10 can be computed using the method of washers via an integral v = ["40) dy where a = 0 .b = 10 and A(y) = pily/10^2-pi(sqrty1/2 The volume of this solid can also be computed using cylindrical shells via an integral v = ["avde where a = and A(x) = In either case, the...
Please solve for number 8. Thank you!!
7-10. Use the region R that is bounded by the graphs of y x-4, and y = 1 to complete the exercises. + 4 Region R is revolved about the x-axis to form a solid of revolution whose cross sections are washers. 7. a. What is the outer radius of a cross section of the solid at a point x in [0, 4]? b. What is the inner radius of a cross section...